Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 29

$\dfrac{130000}{999}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. Re-arrange the given series as: $130.130130...=130 +0.130 (0.001) +130(0.001)^2 +....$ First term $a_1=130$ and Common ratio $r=0.001$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{130}{1-0.001}$ Hence, $S_n=\dfrac{130000}{999}$